i_mca: Incremental Multiple Correspondence Analysis (MCA)

In idm: Incremental Decomposition Methods

Incremental Multiple Correspondence Analysis (MCA)

Description

This function computes the Multiple Correspondence Analysis (MCA) solution on the indicator matrix using two incremental methods described in Iodice D'Enza & Markos (2015)

Usage

i_mca(data1, data2, method=c("exact","live"), current_rank, nchunk = 2, 
 ff = 0, disk = FALSE)

Arguments

data1	Matrix or data frame of starting data or full data if data2 = NULL
data2	Matrix or data frame of incoming data
method	String specifying the type of implementation: "exact" or "live". "exact" refers to the case when all the data is available from the start and dimension reduction is based on the method of Hall et al. (2002). "live" refers to the case when new data comes in as data flows and dimension reduction is based on the method of Ross et al. (2008). The main difference between the two approaches lies in the calculation of the column margins of the input matrix. For the "exact" approach, the analysis is based on the "global" margins, that is, the margins of the whole indicator matrix, which is available in advance. For the "live" approach, the whole matrix is unknown and the global margins are approximated by the "local" margins, that is, the average margins of the data analysed insofar. A detailed description of the two implementations is provided in Iodice D' Enza & Markos (2015).
current_rank	Rank of approximation or number of components to compute; if empty, the full rank is used
nchunk	Number of incoming data chunks (equal splits of 'data2', default = 2) or a Vector with the row size of each incoming data chunk
ff	Number between 0 and 1 indicating the "forgetting factor" used to down-weight the contribution of earlier data blocks to the current solution. When ff = 0 (default) no forgetting occurs; applicable only when method ="live"
disk	Logical indicating whether then output is saved to hard disk

Value

rowpcoord	Row principal coordinates
colpcoord	Column principal coordinates
rowcoord	Row standard coordinates
colcoord	Column standard coordinates
sv	Singular values
inertia.e	Percentages of explained inertia
levelnames	Column labels
rowctr	Row contributions
colctr	Column contributions
rowcor	Row squared correlations
colcor	Column squared correlations
rowmass	Row masses
colmass	Column masses
nchunk	A copy of nchunk in the return object
disk	A copy of disk in the return object
ff	A copy of ff in the return object
allrowcoord	A list containing the row principal coordinates produced after each data chunk is analyzed; returned only when disk = FALSE
allcolcoord	A list containing the column principal coordinates on the principal components produced after each data chunk is analyzed; returned only when disk = FALSE
allrowctr	A list containing the row contributions after each data chunk is analyzed; returned only when disk = FALSE
allcolctr	A list containing the column contributions after each data chunk is analyzed; returned only when disk = FALSE
allrowcor	A list containing the row squared correlations produced after each data chunk is analyzed; returned only when disk = FALSE
allcolcor	A list containing the column squared correlations produced after each data chunk is analyzed; returned only when disk = FALSE

References

Hall, P., Marshall, D., & Martin, R. (2002). Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition. Image and Vision Computing, 20(13), 1009-1016.

Iodice D' Enza, A., & Markos, A. (2015). Low-dimensional tracking of association structures in categorical data, Statistics and Computing, 25(5), 1009–1022.

Iodice D'Enza, A., Markos, A., & Buttarazzi, D. (2018). The idm Package: Incremental Decomposition Methods in R. Journal of Statistical Software, Code Snippets, 86(4), 1–24. DOI: 10.18637/jss.v086.c04.

Ross, D. A., Lim, J., Lin, R. S., & Yang, M. H. (2008). Incremental learning for robust visual tracking. International Journal of Computer Vision, 77(1-3), 125–141.

See Also

update.i_mca, i_pca, update.i_pca, add_es

Examples

##Example 1 - Exact case
data("women", package = "idm")
nc = 5 # number of chunks
res_iMCAh = i_mca(data1 = women[1:300,1:7], data2 = women[301:2107,1:7]
,method = "exact", nchunk = nc)
#static MCA plot of attributes on axes 2 and 3
plot(x = res_iMCAh, dim = c(2,3), what = c(FALSE,TRUE), animation = FALSE)

#\donttest is used here because the code calls the saveLatex function of the animation package 
#which requires ImageMagick or GraphicsMagick and 
#Adobe Acrobat Reader to be installed in your system 
#Creates animated plot in PDF for objects and variables
plot(res_iMCAh, animation = TRUE, frames = 10, movie_format = 'pdf')


##Example 2 - Live case
data("tweet", package = "idm")
nc = 5
#provide attributes with custom labels
labels = c("HLTN", "ICN", "MRT","BWN","SWD","HYT","CH", "-", "-/+", "+", "++", "Low", "Med","High")
#mimics the 'live' MCA implementation 
res_iMCAl = i_mca(data1 = tweet[1:100,], data2 = tweet[101:1000,],
method="live", nchunk = nc, current_rank = 2)


#\donttest is used here because the code calls the saveLatex function of the animation package 
#which requires ImageMagick or GraphicsMagick and 
#Adobe Acrobat Reader to be installed in your system 
#See help(im.convert) for details on the configuration of ImageMagick or GraphicsMagick.
#Creates animated plot in PDF for observations and variables
plot(res_iMCAl, labels = labels, animation = TRUE, frames = 10, movie_format = 'pdf')

idm documentation built on July 12, 2022, 1:05 a.m.